Solve for $x$ and $y$ using elimination. $\begin{align*}5x+3y &= -7 \\ 2x+y &= -5\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-1$ and the bottom equation by $3$ $\begin{align*}-5x-3y &= 7\\ 6x+3y &= -15\end{align*}$ Add the top and bottom equations. $x = -8$ $x = -8$ Substitute $-8$ for $x$ in the top equation. $5( -8)+3y = -7$ $-40+3y = -7$ $3y = 33$ $y = 11$ The solution is $\enspace x = -8, \enspace y = 11$.